(4/3)+(1/3)x-2=2x

Solution for (4/3)+(1/3)x-2=2x equation:

(4/3)+(1/3)x-2=2x

We move all terms to the left:

(4/3)+(1/3)x-2-(2x)=0


Domain of the equation: 3)x!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

(+1/3)x-2x-2+(+4/3)=0

We add all the numbers together, and all the variables

-2x+(+1/3)x-2+(+4/3)=0

We multiply parentheses

x^2-2x-2+(+4/3)=0

We get rid of parentheses

x^2-2x-2+4/3=0

We multiply all the terms by the denominator


x^2*3-2x*3+4-2*3=0

We add all the numbers together, and all the variables

x^2*3-2x*3-2=0

Wy multiply elements

3x^2-6x-2=0

a = 3; b = -6; c = -2;
Δ = b2-4ac
Δ = -62-4·3·(-2)
Δ = 60
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{60}=\sqrt{4*15}=\sqrt{4}*\sqrt{15}=2\sqrt{15}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-6)-2\sqrt{15}}{2*3}=\frac{6-2\sqrt{15}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+2\sqrt{15}}{2*3}=\frac{6+2\sqrt{15}}{6}
$